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Optimal Scores: An Alternative to Parametric Item Response Theory and Sum Scores

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  • Marie Wiberg

    (Umeå University)

  • James O. Ramsay

    (McGill University)

  • Juan Li

    (McGill University)

Abstract

The aim of this paper is to discuss nonparametric item response theory scores in terms of optimal scores as an alternative to parametric item response theory scores and sum scores. Optimal scores take advantage of the interaction between performance and item impact that is evident in most testing data. The theoretical arguments in favor of optimal scoring are supplemented with the results from simulation experiments, and the analysis of test data suggests that sum-scored tests would need to be longer than an optimally scored test in order to attain the same level of accuracy. Because optimal scoring is built on a nonparametric procedure, it also offers a flexible alternative for estimating item characteristic curves that can fit items that do not show good fit to item response theory models.

Suggested Citation

  • Marie Wiberg & James O. Ramsay & Juan Li, 2019. "Optimal Scores: An Alternative to Parametric Item Response Theory and Sum Scores," Psychometrika, Springer;The Psychometric Society, vol. 84(1), pages 310-322, March.
    • Handle: RePEc:spr:psycho:v:84:y:2019:i:1:d:10.1007_s11336-018-9639-4
    DOI: 10.1007/s11336-018-9639-4
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    References listed on IDEAS

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    1. Natasha Rossi & Xiaohui Wang & James O. Ramsay, 2002. "Nonparametric Item Response Function Estimates with the EM Algorithm," Journal of Educational and Behavioral Statistics, , vol. 27(3), pages 291-317, September.
    2. Carol Woods & David Thissen, 2006. "Item Response Theory with Estimation of the Latent Population Distribution Using Spline-Based Densities," Psychometrika, Springer;The Psychometric Society, vol. 71(2), pages 281-301, June.
    3. J. Ramsay, 1991. "Kernel smoothing approaches to nonparametric item characteristic curve estimation," Psychometrika, Springer;The Psychometric Society, vol. 56(4), pages 611-630, December.
    4. Carol M. Woods & David Thissen, 2006. "Item Response Theory with Estimation of the Latent Population Distribution Using Spline-Based Densities," Psychometrika, Springer;The Psychometric Society, vol. 71(2), pages 281-301, June.
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    Cited by:

    1. James Ramsay & Marie Wiberg & Juan Li, 2020. "Full Information Optimal Scoring," Journal of Educational and Behavioral Statistics, , vol. 45(3), pages 297-315, June.

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